how 0!=1


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Question Number 1740 by tabrez8590@gmail last updated on 11/Sep/15

$h o w 0! = 1$
Commented by 123456 last updated on 11/Sep/15

$1! = 1 \cdot 0!$ $so for it work to 1 them 0! = 1$
	Answered by Rasheed Ahmad last updated on 12/Sep/15

	$P e r m u t a t i o n o f r e l e m e n t s f r o m$ $a s e t o f n e l e m e n t s c a n b e p r o v e d$ $e q u a l t o :$ $P (n, r) = n (n - 1) (n - 2) . . . . (n - r + 1) .$ $F o r r < n t h i s i s e q u i v a l e n t t o :$ $P (n, r) = \frac{n!}{(n - r)!}$ $A s s a i d a b o v e f o r r < n t h e a b o v e$ $t w o f o r m u l a e a r e c o n s i s t e n t .$ $B u t a t r = n t h e a b o v e f o r m u l a e$ $g i v e t h e f o l l o w i n g t w o r e s u l t s$ $r e s p e c t i v e l y :$ $P (n, n) = n!$ $P (n, n) = \frac{n!}{(n - n)!} = \frac{n!}{0!}$ $T o c o n t i n u e c o n s i s t e n c y a t n = r$ $w e a r e f o r c e d t o d e f i n e :$ $0! = 1$ $Rasheed Soomro$
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